Probability mass function problem

1. Jan 24, 2013

mcafej

1. The problem statement, all variables and given/known data
1. The sample space Ω of a certain experiment are the values 1, 2, 3, 4 and
5 and the probability assigned to a possible value w is proportional
to w2.
(a) What is the probability mass function p(w) for this probability
space?
(b) What probability does this mass function assign to the interval
(1; 3]?

2. Relevant equations

3. The attempt at a solution
The hardest part for me to understand is the probabilities being proportional to w2. I believe the probabilities for w are 1/15, 2/15, 3/15, 4/15 and 5/15, but I'm not sure. If somebody could clear this up for me it would really help. What does it mean for w to be proportional to w2?

2. Jan 24, 2013

tiny-tim

hi mcafej!
call them A B C D and E instead of 1 2 3 4 and 5 …

then P(E) = 25P(A), P(D) = 16P(A), P(C) = 9P(A), P(B) = 4P(A)

3. Jan 24, 2013

HallsofIvy

That means that P(1)= k, P(2)= 2k, P(3)= 3k, P(4)= 4k, and P(5)= 5k for some number k.

Use the fact that the probabilities must sum to 1 to find k.

That "interval" is really the set {2, 3} so the probability is P(2)+ P(3).

4. Jan 24, 2013

Ray Vickson

It does NOT say that w is proportional to w^2; it says the probability of w is proportional to w^2. Just give the word "proportional" its usual meaning.